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This is a hypothetical based on a result in Griffiths (which is my level of QM understanding). In it, he derives an "exchange force" - two particles states A and B, a two-particle state composed of these will have a larger RMS for identical fermions and a smaller RMS for identical bosons.

I was wondering how the time evolution of such a system looks. When the particles in in energy eigenstates it's trivial, and the exchange interaction merely keeps them from occupying the same eigenstate. However, for a simple system like two free identical non-interaction fermions, would this produce an acceleration? It seems to me like it would from phenomena like degeneracy pressure.

As a further question - if it does produce an acceleration, this feels like a very force-like phenomenon. Is there a reason physics adopted the term "force" specifically for boson-mediated interactions? I understand the derivations are mathematically very different, but it feels awkward talking about pressures and Hamiltonians relating to something that is not a force.

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